WASHINGTON -- Officials inside the Obama administration have grown discouraged by the abruptness with which the news over the killing of Osama bin Laden has turned into a debate over the efficacy of harsh interrogation techniques and torture.

Just days after the al Qaeda leader was killed in a compound in Abbottabad, Pakistan, the political conversation has shifted from the implications of the assassination to questions of whether the waterboarding of valuable detainees was crucial in gathering intelligence on bin Laden's whereabouts.

Defenders of the interrogation technique raised the issue, earning write-ups in several high-profile publications, including The New York Times and Time magazine. It was also put forward in most bin Laden-related news interviews with Obama officials. The problem, those officials stress, is that questioning the effectiveness of waterboarding in the bin Laden case oversimplifies a complex issue to which there may not be any concrete answers.

"There is no possible way to know for sure," said one senior Obama administration official. "Even if waterboarding did produce something -- and that is debatable, the timeline seems very unclear -- it is impossible to say whether interrogation absent it would have produced the same thing. It might have. Lots of detainees provided [intelligence]."

White House spokesman Tommy Vietor was more directly dismissive. "I think this is a distraction from the broader picture, which is that this achievement was the result of years of painstaking work by our intelligence community that drew from multiple sources," he said. "It's impossible to know whether information obtained by EITs [enhanced interrogation techniques] could have been obtained by other forms of interrogation."

By most accounts, harsh interrogation measures including waterboarding did not play a role in helping to track bin Laden's whereabouts or his associates. According to the Times, in 2002 and 2003 "interrogators first heard about a Qaeda courier who used the nom de guerre Abu Ahmed al-Kuwaiti" -- the same courier who would ultimately lead the CIA to bin Laden's location. But, the Times reported, "his name was just one tidbit in heaps of uncorroborated claims."

Sen. Bob Graham (D-Fla.) was the top Democrat on the Senate Intelligence Committee at that time (he would serve in that capacity till January of 2003). Though Graham was well known on the Hill for his copious and detailed note-taking, he said Wednesday in an interview with The Huffington Post that he had no recollection of ever being briefed about a courier or an associate of bin Laden's who could help lead to the al Qaeda leader's location.

Sen. Carl Levin (D-Mich.), who chairs the Senate Armed Services Committee, produced a 263-page report in 2009 on the treatment of detainees in U.S. custody in the years following 9/11. He too dismissed the idea that the interrogation techniques used at that time were efficacious. "If they had any information under the Bush administration that could have led to bin Laden it would have been terribly neglectful for them not to use it," Levin noted in an interview on the "Bill Press Show."

The confirmation of the courier's significance appears to have come in 2004, from an al Qaeda operative who was not waterboarded: Hassan Ghul.

There are, of course, equally adamant defenders of enhanced interrogation techniques. Peter Wehner, former deputy assistant to the president and director of the Bush White House Office of Strategic Initiatives, wrote in Commentary magazine, "It appears that arguably the greatest achievement of the Obama administration, the killing of Osama bin Laden, was the result -- at least in part -- of policies that Obama himself was hyper-critical of."

Jose Rodriguez, who ran the CIA's Counter-Terrorism Center from 2002 to 2005, said that information obtained from top al-Qaeda leaders Khalid Sheikh Mohammad and Abu Faraj al-Libbi -- two individuals subjected to "enhanced interrogation techniques" -- "was the lead information that eventually led to the location of [bin Laden's] compound and the operation that led to his death."

But even former Defense Secretary Donald Rumsfeld stressed that "it was not harsh treatment and it was not waterboarding" that led to the information that, in turn, informed the intelligence community of bin Laden's whereabouts. Rumsfeld has since insisted that harsh interrogations did play a role in intelligence gathering.

Bush administration alums' inability to come to some sort of quick waterboarding consensus underscores why Obama administration officials feel the topic is a distraction. Abu Faraj al-Libbi, the senior administration official noted, "was not waterboarded." Al-Libbi's interrogation did include harsh measures, but was distinct in technique from that of Mohammed.

Rather than debate the usefulness of waterboarding, the White House would rather promote the changes the Obama has championed with respect to processing and acting upon intelligence, as well as the president's vision of a policy that considers Afghanistan and Pakistan inter-connected.

Graham argues the key ingredient to finding bin Laden may not have been, necessarily, the interrogation methods used on detainees but rather how U.S. personnel were able to use the information they received.

"That is the much more significant factor in terms of the flawless success of that operation," the Graham said of the shooting of bin Laden. "This was an operation that was apparently jointly planned -- the actual tactical decisions were made by the CIA, but the people on the ground were Navy SEALS." He said the reorganization of military departments to focus on central commands "has allowed the mission to be the most dominant factor."